Azerbaijan National Academy of Sciences

At a regular meeting of the Presidium of the Azerbaijan National Academy of Sciences, which was held on March 14, a scientific report was presented by the head of the Nonharmonic Analysis Department of the Institute of Mathematics and Mechanics, corresponding member of ANAS Bilal Bilalov on "Some modern fields of mathematics" was listening.

He noted that, the accelerated development of computer science in the modern period contributes to the emergence of new fields of application of mathematics. So, the accelerated development of computer science has led to the creation of new mathematical methods that are used in nature and various spheres of public life.

B.Bilalov said that, along with such traditional spheres of application of classical mathematics as Fourier analysis, differential equations and arithmetic methods, in our country in recent years such areas as mathematics of risk (or actuarial mathematics), the theory of materiality, cluster analysis, discriminant analysis, factor analysis. The development of these spheres is directly related to the development of such methods as neural network, uncertainty estimation (entropy), fuzzy sets theory, wavelet analysis, frame theory, etc.

The speaker noted that the main interest in wavelet analysis arose in the 80s the last century after the publication of the works of French scientists Grossman and Morle in the study of seismic and acoustic signals. In comparison with the classical Fourier analysis, wavelet analysis has more advantages in terms of application. The main essence of the approximation theory, to which the wavelet analysis relates, consists of direct and inverse wavelet transformations.

The scientist said that over the past 10 years, extensive research in these fields has been organized at the Institute of Mathematics and Mechanics, scientific cooperation has been established with the relevant organizations of the republic, as well as in the US, Russia and Ukraine. He noted that, based on the recommendations of the President of the Republic of Azerbaijan Ilham Aliyev in connection with the development of the space industry and the use of satellite data in relevant identification issues, he announced the 70th anniversary of ANAS, scientific programs "Application of the theory of frames and wavelet analysis in seismology and other areas in the processing of signals "and" Approach in the neural network and some frame issues". The programs were supported by the Presidium of ANAS, a corresponding group was formed, and the laboratory "Mathematical Problems of Signal Processing" was established at the Institute. He stressed that about 20 articles written on the basis of research results that were conducted within the framework of the Scientific Programs of ANAS were published in the journals included in the database of the agency "Clarivate Analytics". Two methodological indexes have also been published: "Signals. Classification. Wavelet analysis "and" Mathematical methods for identifying solonetsousness of soils by satellite data ".

B.Bilalov said that a number of works done on the application of wavelet analysis, points to the important scientific and technical significance of research conducted in this field. For the continuation of the studies satellite descriptions of the territory of Azerbaijan received from the LandSat satellite in accordance with the blue, green, red and NIR spectral channels and covering 1999-2017 are collected, statistical studies based on satellite data on specific territories were conducted. He added that this year the country provides for the implementation of such activities as the creation of a ground measurement database and a working statistical database of satellite data in accordance with the selected territory, the determination of soil classification indicators, the selection or determination of solonetsous indices, and the creation of appropriate software.

After listening to the report and announcing the answers to the questions, the Presidium recognized the report as satisfactory. According to the adopted resolution, research in applied mathematics was recognized as one of the priority scientific directions in Azerbaijan. Taking into account the interdisciplinary and multidisciplinary nature of research in applied mathematics, the Department of Physical, Mathematical and Technical Sciences of ANAS was commissioned to expand cooperation between scientific institutions conducting research in this field, to strengthen international cooperation with the leading scientific centers of the world, in choosing themes for dissertations of undergraduates and doctoral students prefer topics dedicated to topical problems of applied mathematics, applied mathematics, implement appropriate training activities in the field of applied mathematics in preparation for highly skilled personnel abroad on government programs, etc.

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